qineq {rquest} | R Documentation |
Hypothesis Tests and Confidence Intervals for Quantile-based Inequality Measures
Description
carry out hypothesis tests and obtain associated confidence intervals for quantile based inequality measures
Usage
qineq(
x,
y = NULL,
J = 100,
measure = "QRI",
alternative = c("two.sided", "less", "greater"),
quantile.type = 8,
var.method = "qor",
conf.level = 0.95,
true.ineq = 0.5,
...
)
Arguments
x |
a numeric vector of data values. |
y |
an optional second vector of data values for two-sample testing. |
J |
number of grid points |
measure |
quantile based inequality measure to be used. Either "QRI" (default) or "G2".(See details). |
alternative |
a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". |
quantile.type |
argument for the quantile function. Default is set to 8 so that output is consistent with default quantile function use and other functions such as IQR (see help file for |
var.method |
approach use to estimate the quantile density function. Either "qor"(default) or "density".(See details). |
conf.level |
coverage for the estimated confidence interval. |
true.ineq |
the specified hypothesized value of the inequality measure or the difference of the inequality depending on whether it was a one-sample test or a two-sample test. |
... |
additional arguments to be passed to function qcov when var.method = “density” is used. |
Details
This function performs hypothesis testing and calculates the corresponding confidence intervals for inequality measures based on quantiles.
The available options for quantile based measures in argument measure
are shown below.
-
QRI
: Quantile Ratio Index (Prendergast & Staudte, 2018). This is the default choice. -
G2
: Quantile variant of the Gini index (Prendergast & Staudte, 2016a).
The default var.method="qor"
is to estimate the probability density function directly using the lognormal Quantile Optimality Ratio (QOR)
for choosing a suitable bandwidth (Prendergast & Staudte,2016b). Alternatively, the variances can be
estimated by inverting a density estimator evaluated at the quantiles and this can be done using var.method = "density"
. If var.method = "density"
,
then the function density is used to estimate the probability density function which is needed for the calculation of the covariance matrix using function qcov.
If needed, additional arguments can be passed to density (see ?density for details on possible additional arguments).
For more information and further examples, see Prendergast, Dedduwakumara & Staudte (2024)
Value
hypothesis test results and associated confidence interval (a list with class "htest")
References
Prendergast, L.A., & Staudte, R.G. (2016a). Quantile versions of the Lorenz curve. Electronic Journal of Statistics, 10(2), 1896 – 1926.
Prendergast, L. A., & Staudte, R. G. (2016b). Exploiting the quantile optimality ratio in finding confidence intervals for quantiles. Stat, 5(1), 70-81
Prendergast, L. A., & Staudte, R. G. (2018). A simple and effective inequality measure. The American Statistician, 72(4), 328-343.
Prendergast, L. A., Dedduwakumara, D.S. & Staudte, R.G. (2024) rquest: An R package for hypothesis tests and confidence intervals for quantiles and summary measures based on quantiles, preprint, pages 1-13
Examples
# Create some data
x <- c(8.43,7.08,8.79,8.88,7.87,5.94,8.79,5.46,8.11,7.08)
y <- c(13.44,13.65,14.77,9.51,14.07,10.92,11.59,13.42,8.93,10.88)
# Two sample hypothesis test for the QRI measure
qineq(x,y)